PS = PR+RS
PS = 18.8+13.7 = 32.5
Answer:
60
Step-by-step explanation:
You would just plug everything in so you get -5(-2-(-5)(-2)) which can be reduced so -5(-12) which is 60
Let <em>a</em> and <em>b</em> be the zeroes of <em>x</em>² + <em>kx</em> + 12 such that |<em>a</em> - <em>b</em>| = 1.
By the factor theorem, we can write the quadratic in terms of its zeroes as
<em>x</em>² + <em>kx</em> + 12 = (<em>x</em> - <em>a</em>) (<em>x</em> - <em>b</em>)
Expand the right side and equate the coefficients:
<em>x</em>² + <em>kx</em> + 12 = <em>x</em>² - (<em>a</em> + <em>b</em>) <em>x</em> + <em>ab</em>
Then
<em>a</em> + <em>b</em> = -<em>k</em>
<em>ab</em> = 12
The condition that |<em>a</em> - <em>b</em>| = 1 has two cases, so without loss of generality assume <em>a</em> > <em>b</em>, so that |<em>a</em> - <em>b</em>| = <em>a</em> - <em>b</em>.
Then if <em>a</em> - <em>b</em> = 1, we get <em>b</em> = <em>a</em> - 1. Substitute this into the equations above and solve for <em>k</em> :
<em>a</em> + (<em>a</em> - 1) = -<em>k</em> → 2<em>a</em> = 1 - <em>k</em> → <em>a</em> = (1 - <em>k</em>)/2
<em>a</em> (<em>a</em> - 1) = 12 → (1 - <em>k</em>)/2 • ((1 - <em>k</em>)/2 - 1) = 12
→ (1 - <em>k</em>)²/4 - (1 - <em>k</em>)/2 = 12
→ (1 - <em>k</em>)² - 2 (1 - <em>k</em>) = 48
→ (1 - 2<em>k</em> + <em>k</em>²) - 2 (1 - <em>k</em>) = 48
→ <em>k</em>² - 1 = 48
→ <em>k</em>² = 49
→ <em>k</em> = ± √(49) = ±7
7 x 6 = $52
there will be no kids attending haha.
- (A) The mainsail foot is 13 feet long, the luff is 10 feet long, the leach is 6.93 feet long, and the mainsail area is 64.85 ft².
- (B) The mainsail foot is 13 feet long, the luff is 10 feet long, and the luff forms a 50° angle with the leach at the head, requiring the length of the leach and the area of the mainsail.
<h3>
What exactly is sines law?</h3>
- The law of sines refers to the ratio of a triangle's side length to the sine of the opposite angle, which is the same for all sides.
- SinA/a = SinB/b = SinC/c
- Where A, B, and C represent the triangle's angle and a,b, and c represent the opposite sides of the triangle's angle.
So, Part A:
By employing the sines law,
- SinA/10 = SinB/13
- SinA/10 = Sin50/13
- A = 36.10
- C = 180-(180-36.10)
- C = 93.90
So,
- Sin36.10 / a = Sin50/ b = Sin93.90/c
- Sin36.10 / 10 = Sin50/ 13 = Sin93.90/c
- c = Sin93.90 × 13 ÷ Sin50
- c = 16.93 ft
Now, Part B:
Area of the mainsail:
- = 1/2 × abSinC
- = 1/2 × 10 × 13 × Sin93.90
- = 64.85
Therefore, the answers to both parts are:
- (A) The mainsail foot is 13 feet long, the luff is 10 feet long, the leach is 6.93 feet long, and the mainsail area is 64.85 ft².
- (B) The mainsail foot is 13 feet long, the luff is 10 feet long, and the luff forms a 50° angle with the leach at the head, requiring the length of the leach and the area of the mainsail.
Know more about sines law here:
brainly.com/question/27174058
#SPJ4
The complete question is given below:
A sailmaker is designing a mainsail for a newly constructed sailboat. The mainsail foot is 13 feet long, the luff is 10 feet long, and the luff makes a 50° angle at the head with the leach.
Part A: Determine the length of the leach.
Part B: Find the area of the mainsail.
PLS HELP :) 50 POINTS!!!
